Stability conditions for refractive partially integrable piecewise smooth vector fields

Detalhes bibliográficos
Autor(a) principal: Buzzi, Claudio A. [UNESP]
Data de Publicação: 2022
Outros Autores: Rodero, Ana Livia [UNESP], Teixeira, Marco A.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.physd.2022.133462
http://hdl.handle.net/11449/240620
Resumo: In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our main goal is to study stability problems inside the class of 3−dimensional refractive piecewise smooth vector fields. Our concern is to study refractive vector fields that admit a first integral that leaves invariant any sphere centered at the origin. Global stability conditions on generic one-parameter families of refractive piecewise smooth vector fields on a two-dimensional sphere are presented and used to prove our main result, which establishes necessary conditions for the structural stability inside that class.
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spelling Stability conditions for refractive partially integrable piecewise smooth vector fieldsIntegrabilityPeixoto's theoremRefractive piecewise smooth vector fieldsStructural stabilityIn this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our main goal is to study stability problems inside the class of 3−dimensional refractive piecewise smooth vector fields. Our concern is to study refractive vector fields that admit a first integral that leaves invariant any sphere centered at the origin. Global stability conditions on generic one-parameter families of refractive piecewise smooth vector fields on a two-dimensional sphere are presented and used to prove our main result, which establishes necessary conditions for the structural stability inside that class.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Estadual Paulista (UNESP) Instituto de Biociências Letras e Ciências ExatasUniversidade Estadual de Campinas Instituto de Matemática Estatística e Computação CientíficaUniversidade Estadual Paulista (UNESP) Instituto de Biociências Letras e Ciências ExatasCNPq: 2017/08779-8CNPq: 2018/13481-0CNPq: 2019/00440-7CNPq: 2019/10269-3CNPq: 304798/2019-3Universidade Estadual Paulista (UNESP)Buzzi, Claudio A. [UNESP]Rodero, Ana Livia [UNESP]Teixeira, Marco A.2023-03-01T20:25:25Z2023-03-01T20:25:25Z2022-11-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.physd.2022.133462Physica D: Nonlinear Phenomena, v. 440.0167-2789http://hdl.handle.net/11449/24062010.1016/j.physd.2022.1334622-s2.0-85135709894Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysica D: Nonlinear Phenomenainfo:eu-repo/semantics/openAccess2023-03-01T20:25:25Zoai:repositorio.unesp.br:11449/240620Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-03-01T20:25:25Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Stability conditions for refractive partially integrable piecewise smooth vector fields
title Stability conditions for refractive partially integrable piecewise smooth vector fields
spellingShingle Stability conditions for refractive partially integrable piecewise smooth vector fields
Buzzi, Claudio A. [UNESP]
Integrability
Peixoto's theorem
Refractive piecewise smooth vector fields
Structural stability
title_short Stability conditions for refractive partially integrable piecewise smooth vector fields
title_full Stability conditions for refractive partially integrable piecewise smooth vector fields
title_fullStr Stability conditions for refractive partially integrable piecewise smooth vector fields
title_full_unstemmed Stability conditions for refractive partially integrable piecewise smooth vector fields
title_sort Stability conditions for refractive partially integrable piecewise smooth vector fields
author Buzzi, Claudio A. [UNESP]
author_facet Buzzi, Claudio A. [UNESP]
Rodero, Ana Livia [UNESP]
Teixeira, Marco A.
author_role author
author2 Rodero, Ana Livia [UNESP]
Teixeira, Marco A.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Buzzi, Claudio A. [UNESP]
Rodero, Ana Livia [UNESP]
Teixeira, Marco A.
dc.subject.por.fl_str_mv Integrability
Peixoto's theorem
Refractive piecewise smooth vector fields
Structural stability
topic Integrability
Peixoto's theorem
Refractive piecewise smooth vector fields
Structural stability
description In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our main goal is to study stability problems inside the class of 3−dimensional refractive piecewise smooth vector fields. Our concern is to study refractive vector fields that admit a first integral that leaves invariant any sphere centered at the origin. Global stability conditions on generic one-parameter families of refractive piecewise smooth vector fields on a two-dimensional sphere are presented and used to prove our main result, which establishes necessary conditions for the structural stability inside that class.
publishDate 2022
dc.date.none.fl_str_mv 2022-11-15
2023-03-01T20:25:25Z
2023-03-01T20:25:25Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.physd.2022.133462
Physica D: Nonlinear Phenomena, v. 440.
0167-2789
http://hdl.handle.net/11449/240620
10.1016/j.physd.2022.133462
2-s2.0-85135709894
url http://dx.doi.org/10.1016/j.physd.2022.133462
http://hdl.handle.net/11449/240620
identifier_str_mv Physica D: Nonlinear Phenomena, v. 440.
0167-2789
10.1016/j.physd.2022.133462
2-s2.0-85135709894
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physica D: Nonlinear Phenomena
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1803046434123022336

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